Partial Derivatives of ln(x+y)/(xy)

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SUMMARY

The discussion focuses on finding the mixed partial derivative fxy of the function f(x,y) = ln(x+y)/(xy). Participants suggest rewriting the function using logarithmic properties, specifically f(x,y) = ln(x+y) - ln(xy) = ln(x+y) - ln(x) - ln(y). This transformation simplifies the differentiation process, allowing for easier computation of the mixed partial derivatives.

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  • Understanding of partial derivatives
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  • Knowledge of multivariable calculus
  • Basic proficiency in differentiation techniques
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  • Study the process of finding mixed partial derivatives
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Students and professionals in mathematics, particularly those studying calculus and multivariable functions, as well as educators looking for examples of applying logarithmic properties in differentiation.

littlesohi
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I need help with this one:

Find fxy in:

ln(x+y)/(xy) .. the ln applies to the whole problem.
 
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littlesohi said:
I need help with this one:

Find fxy in:

ln(x+y)/(xy) .. the ln applies to the whole problem.
Well.

You might rewrite this using the prortyies of the logarithm, say:
f(x,y)=ln(x+y)-ln(xy)=ln(x+y)-ln(x)-ln(y)
 

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